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. 2020 Oct 7;7(19):3521-3532.
doi: 10.1039/D0QI00771D. Epub 2020 Jul 29.

Magnetic hysteresis and strong ferromagnetic coupling of sulfur-bridged Dy ions in clusterfullerene Dy2S@C82

Denis Krylov  1   2 , Georgios Velkos  1 , Chia-Hsiang Chen  1   3 , Bernd Büchner  1 , Aram Kostanyan  4 , Thomas Greber  4 , Stanislav M Avdoshenko  1 , Alexey A Popov  1
Affiliations

Magnetic hysteresis and strong ferromagnetic coupling of sulfur-bridged Dy ions in clusterfullerene Dy2S@C82

Denis Krylov et al. Inorg Chem Front. .

Abstract

Two isomers of metallofullerene Dy2S@C82 with sulfur-bridged Dy ions exhibit broad magnetic hysteresis with sharp steps at sub-Kelvin temperature. Analysis of the level crossing events for different orientations of a magnetic field showed that even in powder samples, the hysteresis steps caused by quantum tunneling of magnetization can provide precise information on the strength of intramolecular Dy⋯Dy inter-actions. A comparison of different methods to determine the energy difference between ferromagnetic and antiferromagnetic states showed that sub-Kelvin hysteresis gives the most robust and reliable values. The ground state in Dy2S@C82 has ferromagnetic coupling of Dy magnetic moments, whereas the state with antiferromagnetic coupling in C s and C 3v cage isomers is 10.7 and 5.1 cm-1 higher, respectively. The value for the C s isomer is among the highest found in metallofullerenes and is considerably larger than that reported in non-fullerene dinuclear molecular magnets. Magnetization relaxation times measured in zero magnetic field at sub-Kelvin temperatures tend to level off near 900 and 3200 s in C s and C 3v isomers. These times correspond to the quantum tunneling relaxation mechanism, in which the whole magnetic moment of the Dy2S@C82 molecule flips at once as a single entity.

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Conflict of interest statement

Conflicts of interest There are no conflicts to declare.

Figures

Fig. 1
Fig. 1
(a) Molecular structures of Dy2S@C82-C s and Dy2S@C82-C 3v (Dy is green, S is yellow, the carbon cage is transparent gray, and green arrows show one of the possible orientations of magnetic moments of Dy ions in the ground state doublet); two fullerene isomers have different orientation of pyracelene units highlighted in light red; C–C bonds which undergo 90° rotation in Stone–Wales transformation connecting these two isomers are shown in red. (b) Schematic description of two quasi-doublets defined as ferromagnetically (FM) and antiferromagnetically (AFM) coupled, green arrows denote magnetic moments of individual Dy ions, whereas red and dark blue arrows are total moment of the Dy2S@C82 molecule, the values are computed for the Dy–S–Dy angle of 105°; dashed arrows show the main low-temperature mechanisms of the relaxation of magnetization, including quantum tunneling of magnetization (QTM), Orbach mechanism via AFM-coupled state with effective barrier Ueff, and Raman mechanism via virtual state of higher energy. (c) and (d) show Zeeman diagrams for Dy2S@C82 for two arbitrary orientations of the molecule versus the magnetic field, in (c) the total magnetic moment of the FM state is close to the parallel orientation, whereas in (d) orientation is close to perpendicular; red and blue arrows show orientations of the magnetic moments for FM and AFM states, thick lines highlight the ground state in a given field range, and letters A, B, A’, and B’ mark different kinds of level crossing discussed in the text (each of these crossings is actually an avoided crossing with a certain tunneling gap, but showing this would overwhelm the figures with details). (e and f) Histograms (binning 0.05 T) of the crossing events of types A and B’ in C s and C 3v isomers of Dy2S@C82 computed for an ensemble of 105 randomly oriented molecules overlaid with experimental hysteresis curves recorded at 0.41 K.
Fig. 2
Fig. 2
Magnetic hysteresis of (a) Dy2S@C82-C s and (b) Dy2S@C82-C 3v measured at T = 0.41 K and compared to some higher-temperature curves recorded until the hysteresis is closed. Sweep rates 2.9 mT s−1 for T = 2 K and above, and 3.3 mT s−1 for T = 0.41 K. QTM0, QTMA, and asterisk denote the features appearing because of the level crossing in Zeeman diagrams and are explained in the text.
Fig. 3
Fig. 3
Equilibrium magnetization curves of (a) Dy2S@C82-C s and (b) Dy2S@C82-C 3v measured at temperatures between 2 K and 200 K. Grey dots are experimental values used in the fitting procedure; coloured lines are simulated for powder samples using fitted j 12 and α parameters (j 12 = 0.16 cm−1 and α = 72.3° for Dy2S@C82-C s; j 12 = 0.12 cm−1, α = 75.7° for Dy2S@C82-C 3v). Coloured dots are the fragments of experimental magnetization curves with open hysteresis; these points were not used in the fitting procedure and are shown here to guide the eye. Note that the absolute experimental values of magnetization are not known because of the small sample mass, and the fitting is done for the normalized magnetization curves.
Fig. 4
Fig. 4
Magnetization relaxation times of (a) Dy2S@C82-C s and (b) Dy2S@C82-C 3v. Dark cyan and red dots are DC and AC measurements, solid lines are fits by a combined equation eqn (1), and dashed lines are contributions of QTM, Raman, and Arrhenius processes. The insets show magnification of higher-temperature parts.
Fig. 5
Fig. 5
DFT-computed spin-density distribution (green – “+”, red – “−”) in: (a) Gd2S@C82-C s and Gd2S@C82-C 3v molecules shown with isovalues of ±0.0012 a. u. (b) Gd2S@C82-C s and GdYS@C82-C s with an isovalue of ±0.00012 a. u. (c) Gd2S@C82-C 3v and GdYS@C82-C 3v with an isovalue of ±0.00012 a. u. The isosurfaces in (a) are plotted semitransparent to show positions of metals and sulfur in the endohedral cluster. Computations performed at the PBE0/TZVP level with DKH scalar-relativistic correction and DKH-tailored full-electron basis sets.
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